Skip to main content

Table 7 Results on stable L1-structures

From: A replica exchange Monte Carlo algorithm for protein folding in the HP model

ID E* PERM t e x p MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabdwgaLjabdIha4jabdchaWbqabaaaleqaaaaa@373A@ REMC pm REMC m
L1-1-3 -16 -16 (120 sec) -16 (6 sec) -16 (6 sec)
L1-2-2 -16 -16 (57 sec) -16 (3 sec) -16 (2 sec)
L1-3-1 -16 -16 (28 sec) -16 (3 sec) -16 (3 sec)
L1-1-5 -24 -24 (100 hrs†) -24 (17 min) -24 (14 min)
L1-2-4 -24 -24 (49 hrs†) -24 (9 min) -24 (7 min)
L1-3-3 -24 -23 -24 (7 min) -24 (5 min)
L1-4-2 -24 -24 (49 hrs†) -24 (5 min) -24 (4 min)
L1-3-7 -40 -38 -38 (20 hrs) -38 (20 hrs)
L1-5-5 -40 -38 -38 (16 hrs) -38 (14 hrs)
L1-8-2 -40 -38 -38 (16 hrs) -38 (14 hrs)
  1. The L1-structures proposed in [52] are the most difficult stable structures for REMC to fold. Both PERM and REMC are unable to find the optimal conformations for L1-3-7, L1-5-5, and L1-8-2 after 100, one hour runs. PERM also did not find the optimal conformation for L1-3-3. When only one folding direction of PERM finds the optimal conformation, we report the mean run-time of that direction, denoting this in the table with a †. When best energies found by PERM t 1 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabigdaXaqabaaaleqaaaaa@33F5@ and PERM t 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGqbaucqqGfbqrcqqGsbGucqqGnbqtdaWgaaWcbaGaemiDaq3aaSbaaWqaaiabikdaYaqabaaaleqaaaaa@33F7@ differed (and neither find the optimal solution), the best energy by either is reported and the run-time is omitted. For every instance, 100 independent runs were conducted of 1 CPU hour each. In cases where not every run reached the same energy value after 1 hour, the expected run-time to reach the energy value shown in the table was calculated using the equation detailed by Parkes and Walser [54].